If you are married filing jointly, your standard deduction is $12,400 in year 2014, plus two exemptions at $3,950 each. That means your first $20,300 in income is tax-free. The next $18,150 is at a 10% rate. The next $55,650 is at a 15% rate.
$20,300 (tax free income) / 0.04 withdrawal rate = $507,500 nest egg required.
That means the first $507,500 you can set aside in tax-deferred accounts (401k, traditional IRA, etc.) will be tax free.
$18,150 (10% income) / 0.04 withdrawal rate = $453,750 additional nest egg (10% marginal).
The means the next $453,750 you can set aside in tax-deferred accounts will be taxed at 10%. That means you can set aside 960k in tax deferred accounts that are taxed at 0% or 10%. That is probably close to enough for most people.
$55,650 (15% income) / 0.04 withdrawal rate = $1,391,250 additional nest egg (15% marginal).
That means the next $1.4million you can set aside in tax-deferred accounts will be taxed at 15%. That allows for $2.3 million to be set aside in tax deferred accounts that are taxed at 0%, 10%, or 15%. That is more than enough money to retire on, and that is at a marginal tax rate that is lower than most people are paying during their working years.
That is why I contribute enough to my 401k and IRA in order to keep my marginal tax rate below 25% whenever possible.